One out of 500 people has disease D. You're a doctor and suspect that one of your patients may have that disease. You order a diagnostic test T for that patient. The test is not perfect - it accurately claims the disease is "present" in 80% of the patients who actually have it, and accurately declares the disease as "absent" in 70% of the patients who indeed don't have the disease.

a) If the test result comes back negative (the test says "absence of disease"), what does that mean for your patient -- how likely is he to actually have disease D?

b) How about if the test comes back positive (the test says "disease") -- how likely is he to actually have disease D then?